Unexamined Japanese patent publications No. 2000-350482 and No. 2001-211669 disclose a drive unit in which a cyclic drive voltage is applied to an electromechanical transducer (e.g. piezoelectric element) to oscillate a drive element fixed to one end of the electromechanical transducer at asymmetrical rate so that a movable element frictionally engaged with the drive element can slide on the drive element in a direction and stop at predetermined position. Unexamined Japanese patent publications No. 2003-199374 and No. 2003-203440 disclose a disc type information recording device for CD, DVD and so on which uses said drive unit as a positioning mechanism of a read/write head.
FIG. 8 shows a principle of operation of a conventional drive unit 31. The drive unit 31 has a movable element 34 frictionally engaged with a drive element 33 fixed at the one end to an electromechanical transducer 32 which is fixed to a support element. When the drive voltage is applied, the electromechanical transducer 32 extends or contracts depending on the applied drive voltage. In the case where the electromechanical transducer 32 is extended slowly from the state shown in FIG. 8(A), the drive element 33 is pushed out slowly with the movable element 34 frictionally engaged, causing the movable element 34 to change its absolute position as shown in FIG. 8(B). When the electromechanical transducer 32 is contracted rapidly from the state shown in FIG. 8(B), the drive element 33 is rapidly pulled back, causing the movable element 34 to be left as shown in FIG. 8(C) and displaced relatively against the drive element 33. FIG. 9 shows an ideal waveform of the axial displacement of the drive element 33 for displacement of the movable element 34. Each points A, B, C are corresponding with FIGS. 8(A), 8(B), 8(C). It is preferable to apply the axial displacement in sawtooth waveform to the drive element 33 so that the drive element 33 is pushed out in a constant rate and rapidly pulled back in an opposite direction.
FIG. 10 shows a drive circuit 36 for applying the drive voltage to the electromechanical transducer 32 to operate the drive unit 31. The drive circuit 36 comprises a power source with voltage E(V), two p-channel FETs 37,38, two n-channel FETs 39,40 and a CPU 41 for switching each FETs 37-40. The CPU 41 turns on the gate voltages of FETs 37,40 or of FETs 38,39 alternately so that the electromechanical transducer 32 is applied a drive voltage with a rectangular waveform alternating +E(V) and −E(V). The position of the movable element 34 can be specified by counting the times of the switching (number of pulse). As described in the unexamined Japanese patent publication No. 2001-211669, the frequency of the drive voltage with rectangular waveform is preferably 0.7 times the resonance frequency of the electromechanical transducer 32 and the duty ratio of the rectangular waveform is preferably 0.7 times the electromechanical transducer 32, and the duty ratio is preferably 0.7 in the case of that the movable element 34 must be displaced in a pushed out direction and 0.3 in the case of the movable element 34 must be displaced in a pulled back direction. The fundamental wave e1 and the second harmonic wave e2 of the rectangular wave with a duty ratio of 0.3 can be expressed as below as a result of Fourier transform. The third harmonic wave or higher orders of harmonic waves are omitted because they hardly affect the displacement of the movable element 33.
                              e          ⁢                                          ⁢          1                =                  1.03          ⁢          E          ⁢                                          ⁢                      sin            ⁡                          (                              2                ⁢                π                ⁢                                                                  ⁢                                  fd                  1                                ⁢                t                            )                                                          (        1        )                                          e          ⁢                                          ⁢          2                =                  0.61          ⁢          E          ⁢                                          ⁢                      sin            ⁡                          (                                                4                  ⁢                  π                  ⁢                                                                          ⁢                                      fd                    1                                    ⁢                  t                                -                                  π                  2                                            )                                                          (        2        )            
If the drive element 33 is an absolute rigid body, the transfer characteristic of the axial displacement of the movable element 33 of the drive unit 31 has one resonance frequency as described in the unexamined Japanese patent publication No. 2001-211669. However, the practical drive element 33 has elasticity and the axial displacement at the point of the drive element 33 engaging with the movable element 34 is described in the second order vibration model as shown in FIG. 11. So the transfer characteristic has two resonance frequencies. In the FIG. 11, the electromechanical transducer 32 comprises a spring constant k1, a damping coefficient c1 and a mass m1, and the drive element 33 comprises a spring constant k2, a damping coefficient c2 and a mass m2. In that case, it should be noted that the spring constant k2 and the damping coefficient c2 varies depending on a position where the movable element 34 is engaging frictionally with the drive element 33.
FIG. 12 shows the transfer characteristic of the gain of the axial displacement at the point A of the drive element 33 in responding to the applied sinusoidal voltage (the ratio of the amplitude of vibration to the displacement with DC voltage) and the phase in responding to the applied sinusoidal voltage at the point A in solid lines, also the transfer characteristic at the point B in dashed line. As the movable element 34 is positioned at the point B closer to the electromechanical transducer 32, the characteristic of the drive element 33 gets close to a rigid body and therefore the gain at the second order resonance point becomes lower. As the gain at the higher frequency is lower, the third or higher harmonic wave can not affect the axial displacement. If the first order resonance frequency is f1, the second order resonance frequency is f2, the drive frequency of 0.7 times the frequency of f1 is f1d and the frequency of two times the frequency of f1d is d2d, then at the point A, the gain responding to the sine wave with frequency f1d is G1, the phase responding to f1d is θ1, the gain responding to the sine wave with the frequency of f2d is G2 and the phase responding to f2d is θ2. While at the point B, the gain and the phase responding to the f1d are substantially same as G1 and θ1, the gain responding to the f2d is G2′ smaller than G2 and the phase responding to fd2 is θ2′ delayed from θ2.
The fundamental frequency component x1 and second harmonic component x2 of axial displacement at the point A, and the fundamental frequency component x1′ and second harmonic component x2′ at the point B in responding to e1 and e2 when E=3V are expressed below, in the condition of G1=−144 dB, G2=−150 dB, G2′=−160 dB, θ1=−20°, θ2=−130° and θ2′=−140°.x1=x1′=1.95×10−7 sin(2πfd1t−20°)  (3)x2=5.79×10−8 sin(4πfd1t−220°)  (4)x2′=1.83×10−8 sin(4πfd1t−230°)  (5)
As FIG. 13 shows, the waveform of the axial displacement at the point A of the movable element 33 is a composite waveform shown in a solid line which is obtained by adding the axial displacement x1 responding to the fundamental sine wave as shown in an one dot chain line and the axial displacement x2 responding to the second harmonic wave as shown in a dashed line. As FIG. 14 shows, the waveform of the axial displacement at the point B of the movable element 33 is also a composite waveform obtained by adding x1′ and x2′. The axial displacement at the point A presents a sawtooth waveform which pushes the drive element 33 out slowly and pulls it back rapidly. That is close to the ideal waveform as shown in FIG. 9, causing the effective displacement of the movable element 34. On the other hand, as shown in FIG. 14, the axial displacement at the point B presents a waveform close to a sine wave which has a similar rate of movement in both pushing and pulling directions, resulting in ineffective displacement of the movable element 34. This means that the displacement of the movable element 34 for each cycle of the drive voltage in the conventional drive unit 31 is varied in accordance with the position of the movable element 34.
If the drive unit 31 in which the displacement rate is varied according to the position of movable element 34 as described above is used as a positioning mechanism of a read/write head of a disc type information recording device, the movable element 34 is not displaced in proportion to the count of the switchings of FETs 27-30 by the CPU 41, causing a tracking error.